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The Laplace transform

Author: Richard Bellman; Robert S Roth
Publisher: Singapore : World Scientific, 1984.
Series: Series in modern applied mathematics, v. 3.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Richard Bellman; Robert S Roth
ISBN: 9971966735 9789971966737
OCLC Number: 11954595
Language Note: English.
Notes: Includes index.
Description: xv, 158 pages : illustrations ; 23 cm.
Contents: PREFACE; CONTENTS; Chapter 1 THE LAPLACE TRANSFORM; 1.1 Introduction; 1.2 Functions of a Bounded Variation; 1.3 The Stieltjes Integral; 1.4 Improper Stieltjes Integral; 1.5 The Laplace Transform; 1.6 Existence and Convergence; 1.7 Properties of the Laplace Transform; 1.8 The Inversion of the Laplace Transform; 1.9 The Convolution Theorem; 1.10 Instability of the Inverse of the Laplace Transform; 1.11 The Laplace Transform and Differential Equations; 1.12 Transient Solutions; 1.13 Generating Functions; Problems; Chapter 2 ORDINARY DIFFERENTIAL EQUATIONS; 2.1 Introduction. 2.2 Linear Differential Equations With Constant Coefficients2.3 The Laplace Transform Solution; 2.4 Systems of Linear Differential Equations; 2.5 Mismatched Solutions; 2.6 Behavior Of The Higher Derivatives; 2.7 An Example; Problems; Chapter 3 DIFFERENTIAL-DIFFERENCE EQUATIONS; 3.1 Introduction; 3.2 Examples; 3.3 Types of Differential-Difference Equations; 3.4 Existence and Uniqueness; 3.5 Exponential Solutions; 3.6 Laplace-Transform Solutions; 3.7 Order Of Growth Of Solutions; 3.8 The Characteristic Roots; 3.9 Asymptotic Behavior of the Solution; 3.10 The Shift Theorem. 3.11 Equations of the Neutral and Advanced Types3.12 Linear Systems Of Differential-Difference Equations; 3.13 A Limiting Case For Differential-Difference Equations; Problems; Chapter 4 PARTIAL DIFFERENTIAL EQUATIONS; 4.1 Introduction; 4.2 The Hyperbolic Partial Differential Equation; 4.3 The Parabolic Partial Differential Equation; 4.4 The Elliptic Partial Differential Equation; Chapter 5 THE RENEWAL EQUATION; 5.1 Introduction; 5.2 The Formal Laplace Transform Solution; 5.3 Exponential Bounds on u(t); 5.4 A Convolution Theorem; 5.5 Use of the Contour Integral Representation. 5.6 Some Important Results5.7 Systems of Renewal Equations; 5.8 Branching Processes; Problems; Chapter 6 NUMERICAL INVERSION OF THE LAPLACE TRANSFORM; 6.1 Introduction; 6.2 The Complex Laplace Transform; 6.3 Numerical Quadrature; 6.4 The Legendre Polynomials; 6.5 Numerical Inversion of the Laplace Transform; 6.6 Explicit Inversion Formula; 6.7 Instability of the Inverse of the Laplace Transform; 6.8 Tychonov Regularization; 6.9 Obtaining the Initial Approximation; 6.10 Change of the Time Scale; Problems; SUBJECT INDEX.
Series Title: Series in modern applied mathematics, v. 3.
Responsibility: Richard E. Bellman, Robert S. Roth.

Abstract:

The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.

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"This book is a very valuable addition to the existing literature on the subject." S Conde (Maracaibo) Mathematical Reviews (USA), 1987 "The book presents many useful problems which help the Read more...

 
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